# Generation of unique-sum sets [closed]

I've been beating around the bush for a long time, ever since I've been in StackExchange. Now, I really must come to the point. I have a link here that you people can see (go to about the end of the eighth page)

Given a value for $p$, how will you generate the sequence, moreover, what will the $n$th element in the set be?

Edit Perhaps I should've written this before, never mind... I meant to say, how do I go about generating a unique-sum set with $p$ elements, as the few examples on page 9 (i.e. following part 2.3) show, and when done so, how would I know what the $n$th element in that set would be, considering I won't be looking over the entire thing once I'm done generating the set?

-

## closed as unclear what you're asking by Jonas Meyer, Daniel Robert-Nicoud, TravisJ, Deepak, graydadMay 27 at 2:33

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

Isn't there some way you can explain your question without asking your audience to first read a 16-page paper? –  MJD Apr 4 '12 at 17:00
Aside from the word set in the title, what is the relation to set theory? Can it be understood without reading the said 16 pages long paper? –  Asaf Karagila Apr 4 '12 at 17:04
The relevant content of the paper is all in section 2.3: a "unique-sum set" of positive integers is a set $\{s_1...s_n\}$ for which the only solution to $\sum c_is_i = \sum s_i$ has $c_i = 1$ for each $i$. But I cannot make out what question is being asked. –  MJD Apr 4 '12 at 17:07
The first half of the post mentions beating around the bush and getting to the point. The second half is evasive and unclear. Ironic, no? –  Théophile Apr 4 '12 at 17:15
I am not objecting that you included a link to the paper. My objection is that you did not clearly state a question that can be answered without reading the paper. –  MJD Apr 4 '12 at 17:38

In the example on page 9, the set $U_p$ contains the $p$ numbers $2^p - 2^{p-m}$ for each $m$ in $1\ldots p$. For example, $U_5 = \{ 32-1, 32-2, 32-4, 32-8, 32-16 \} = \{ 16, 24, 28, 30, 31 \}$. Proposition 2 claims that the $U_p$ sets have the unique-sum property. Is this what you were looking for?